Simplify the following expression: $ r = \dfrac{-1}{7} + \dfrac{10n + 4}{-9n - 7} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-9n - 7}{-9n - 7}$ $ \dfrac{-1}{7} \times \dfrac{-9n - 7}{-9n - 7} = \dfrac{9n + 7}{-63n - 49} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{10n + 4}{-9n - 7} \times \dfrac{7}{7} = \dfrac{70n + 28}{-63n - 49} $ Therefore $ r = \dfrac{9n + 7}{-63n - 49} + \dfrac{70n + 28}{-63n - 49} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{9n + 7 + 70n + 28}{-63n - 49} $ $r = \dfrac{79n + 35}{-63n - 49}$ Simplify the expression by dividing the numerator and denominator by -1: $r = \dfrac{-79n - 35}{63n + 49}$